What is the Greatest Common Factor of 38688 and 38700?

Greatest common factor (GCF) of 38688 and 38700 is 12.

GCF(38688,38700) = 12

We will now calculate the prime factors of 38688 and 38700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38688 and 38700.

How to find the GCF of 38688 and 38700?

We will first find the prime factorization of 38688 and 38700. After we will calculate the factors of 38688 and 38700 and find the biggest common factor number .

Step-1: Prime Factorization of 38688

Prime factors of 38688 are 2, 3, 13, 31. Prime factorization of 38688 in exponential form is:

38688 = 2⁵ × 3¹ × 13¹ × 31¹

Step-2: Prime Factorization of 38700

Prime factors of 38700 are 2, 3, 5, 43. Prime factorization of 38700 in exponential form is:

38700 = 2² × 3² × 5² × 43¹

Step-3: Factors of 38688

List of positive integer factors of 38688 that divides 38688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52, 62, 78, 93, 96, 104, 124, 156, 186, 208, 248, 312, 372, 403, 416, 496, 624, 744, 806, 992, 1209, 1248, 1488, 1612, 2418, 2976, 3224, 4836, 6448, 9672, 12896, 19344

Step-4: Factors of 38700

List of positive integer factors of 38700 that divides 38688 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 43, 45, 50, 60, 75, 86, 90, 100, 129, 150, 172, 180, 215, 225, 258, 300, 387, 430, 450, 516, 645, 774, 860, 900, 1075, 1290, 1548, 1935, 2150, 2580, 3225, 3870, 4300, 6450, 7740, 9675, 12900, 19350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38688 and 38700. The biggest common factor number is the GCF number.
So the greatest common factor 38688 and 38700 is 12.

Also check out the Least Common Multiple of 38688 and 38700